Anything is better than a built in soundcard like that, so YES, you need an amp or a better sound card. No one deserves to be left with one such as a Realtek that cares about audio.

That's quite an over-generalization. Will the sound be improved? The answer is maybe.

I have two computers, with two different models of built-in Realtek sound hardware, and they both produce very good audio. To my ears, my Matrix M-Stage and O2+ODAC are generally superior, occasionally but a large margin, , but not always. OTOH, they're never bettered by my built-in audio. My headphones include the DT 990 and HD 650.

There are plenty of badly designed, marginally tested, and/or poorly constructed DAC's and amplifiers. Any reasonable Realtek implementation will be noticeably superior.